= Solution
{c}
When $\alpha>n$, set $\mu=\sqrt{\alpha^2-n^2}>0$. The reduced <ordinary differential equation> is $F''-\mu^2F=0$. Enforcing the same <initial conditions> gives
$$
\boxed{F(t)=\frac{\sinh(\mu t)}\mu,\qquad\mu=\sqrt{\alpha^2-n^2}.}
$$
The corresponding <overdamped> <normal mode> can also be written
$$
y(x,t)=\frac{e^{(-\alpha+\mu)t}-e^{(-\alpha-\mu)t}}{2\mu}\sin(nx).
$$
Both rates in the <exponential functions> are negative because $0<\mu<\alpha$, so the <hyperbolic sine> factor does not prevent decay.
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